Find the Variables

Problem

[[t+1,−8,4],[5,−6,−3]]=[[3,−8,4],[5,x−7,−3]]

Solution

1. Identify the corresponding elements in the two equal matrices. For two matrices to be equal, every corresponding entry must be equal.

2. Set up an equation for the variable t by equating the elements in the first row and first column.

t+1=3

3. Solve for t by subtracting 1 from both sides of the equation.

t=2

4. Set up an equation for the variable x by equating the elements in the second row and second column.

−6=x−7

5. Solve for x by adding 7 to both sides of the equation.

x=1

Final Answer

t=2,x=1

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